The turbine section of a gas turbine engine has circular arrays of blades mounted on rotating disks. The tips of the blades are closely surrounded by a shroud ring formed of a circular array of shroud ring segments. The shroud ring bounds the working gas flow. The ring segments are supported by a radially outer ring structure made of a circular array of support blocks connected to the turbine casing. Each support block may mount multiple ring segments. Each ring segment may have a radially inner lip extending forward of a structural frame on the backside of the ring segment. The term “backside” herein means a radially outer or distal side of a shroud ring component with respect to the turbine axis. The terms “forward”, “front”, “fore”, and “aft” herein mean upstream (forward, front, fore) and downstream (aft) with respect to the working gas flow. The radially inner front lips of the ring segments are more susceptible to heat damage and wear from hot combustion gas, which can intrude to the backside of the lip due to high static and dynamic pressure, especially at stage 1 of the turbine section. Combustion gas can further intrude into gaps between adjacent ring segments. It can cause heat damage, including cyclic thermal expansion fatigue that can initiate cracks and other degradation in the ring segment or support block.